- Allow single (behavior) inheritance (model here is quite a few modern
languages, such as C#, D, ...)
- Allow multiple declarative inheritance (interface like, the
inheritance almost works like this today though)

If, with these restrictions (or maybe only the first), do you think that
it will simplify implementation and make it more feature complete?

I think you'll need to be a bit more specific to elicit a response. What
exactly are you proposing to change?